A quartic bound involving an absolute difference

Proved

WorkbookSource.base_867

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

If $x,y {\ge} 0$ , then prove: $5(x^4+y^4){\ge} (x^2+y^2)(x+y+|x-y|)^2$

Source: InternLM Lean-Workbook, record lean_workbook_867 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_867 (x y : ℝ) (hx: x ≥ 0) (hy: y ≥ 0) : 5 * (x^4 + y^4) ≥ (x^2 + y^2) * (x + y + |x - y|)^2  :=  by sorry

Source